The sperm-tail axonemes of several insect species are known to have accessory microtubules with a diameter greater than that of ordinary cytoplasmatic microtubules. This provides an opportunity to investigate the three-dimensional organization of naturally occurring tubules with more than 13 protofilaments. For this purpose electron micrographs of negatively stained axonemes of a dipteran species, Exechia seriata, and a trichopteran, Limnephilus bipunctatus, were taken for computer analysis. The original micrographs contained long stretches of somewhat curved microtubules that, in a first step, were straightened by an appropriate algorithm. The results were used to determine helical models from spectral analysis, to obtain filtered images of the front and back tubule sides, and to compute three-dimensional reconstructions by Fourier methods. The tubule segments used in the present study were about 500 nm long. All accessory microtubules analyzed consisted of a double-stranded helix of clearly distinguishable heterodimers with a pitch of 16 nm and skewing protofilaments. Most segments of the dipteran accessory tubules consisted of 16 protofilaments, although 15 were found in some images portraying the distal region of the flagellum. The accessory tubules of the trichopteran had 19 protofilaments. The repeat periods that describe the skewness of protofilaments (128 nm for 16 and 320 nm for 19 protofilaments) are in any case considerably thicker than an electron microscopical section which encompasses about 50 nm. It is hence valid to count the number of protofilaments in cross-sectioned axonemes. (C) 1994 Academic Press, Inc.